Problem: Simplify the following expression: $ z = \dfrac{r - 9}{r - 5} + \dfrac{10}{7} $
Answer: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{7}{7}$ $ \dfrac{r - 9}{r - 5} \times \dfrac{7}{7} = \dfrac{7r - 63}{7r - 35} $ Multiply the second expression by $\dfrac{r - 5}{r - 5}$ $ \dfrac{10}{7} \times \dfrac{r - 5}{r - 5} = \dfrac{10r - 50}{7r - 35} $ Therefore $ z = \dfrac{7r - 63}{7r - 35} + \dfrac{10r - 50}{7r - 35} $ Now the expressions have the same denominator we can simply add the numerators: $z = \dfrac{7r - 63 + 10r - 50}{7r - 35} $ $z = \dfrac{17r - 113}{7r - 35}$